The goal of this worksheet is to explore how we may use the line tangent to a function to tell 11s some information about function values. 1. Sketch a graph of f(.'L') = 3:2? as well as the line tangent to x) at 3: = 1' 2. Find the equation of your tangent line. 3. Find the y-coordinate of the point on your tangent line with arr-coordinate 1.1. 4. How do the values of f (1.1) and your answer to #3 compare? 3. Given your graph, explain why your answer to #4 makes sense. 6. Given the graph of the function below sketch the line tangent to your curve at (a, f ((1)). 7. Find the equation of the line that you sketched. Your answer should have a in it. rThis is called the linearzaton of f(3:) at 3: = a. 8. If 5 is close to a: how will the ycoordinate of the point [5, f[b)) and the ycoordinate of the point on your tangent line at I = I} compare? Thus, you may use a linearization of f (3:) at 3: = a. to approximate function values: f (b): for 3) near (1. Using this method to approximate is called linear appmmmaton. Next, you will use linear approximation= that is, use a linearizationT to approximate v97. 9. 1What is the function that you are going to linearize? 10. Now, you need to choose an 3: value that is near 97, but that is easier to work with. 1What 3: value should you choose? 11. Find the linearization of f (3:) (from #9) at the 3: value you choose in #10. 12. Explain how/why you can use the linearization found in #11 to approximate v 97. 13. Use your linearization to approximate V 97. 1 6561' Next, you will use a linearization of f[I) 2 I17 at I = 10 to approximate 14. Find the linearization of f(I) = :14- at I = 10. 1 15. Use the linearization found in #14 to approximate 1. Be very thoughtful about your inputs. 1 6561' Of course5 you could have used a different function when approximating 16. What is another function you might use? 17. In this case= at what 3: value would you choose to do your linearization? 18. Use the linearization of the function chosen in #16 at the I-value chosen in #17 to 1 6561' approximate